A photo-acoustic spectrometer (PAS) is an instrument to measure trace gases, which operates by illuminating the gas with modulated light resonant with the species of interest in a small chamber. The light energy is absorbed, usually exciting molecular vibrational modes. Via collisional exchange, the vibrational energy is transferred to increased molecular kinetic energy, equivalent to a local rise in macroscopic temperature. The local temperature increase induces a pressure wave, which propagates throughout the small chamber and is measured by a microphone.
In a non-resonant chamber the acoustic pressure is P=K(Cp/Cv−1)I/f; where K is a constant depending on the cell geometry and gas; Cp and Cv are the gas specific heats at constant pressure and volume, respectively; I is the light intensity; and f is the light modulation frequency. That the acoustic pressure depends on the period of the light modulation implies there is no well definable acoustic wave front, but rather the entire volume of gas is being heated over a time T/2 where T is f1. Typically f ˜25 Hz. Physically, the pressure inside the chamber is increasing and decreasing at that frequency. At atmospheric pressure and typical chamber length scales of 1 cm the corresponding acoustic frequency would be 33 kHz.
In a resonant photo-acoustic spectrometer, the light is modulated at a frequency equal to a natural resonant frequency of the chamber. For a cube chamber geometry this would be a standing wave mode, with the lowest frequency mode having a wavelength twice the cube's linear dimension. Typical modulation frequencies for resonant chambers are in the kilohertz range. Resonant chambers pump up the standing wave in a coherent fashion, resulting in higher pressure levels and larger microphone signals. Resonant chamber spectrometers can have signal-to-noise ratios orders of magnitude higher than their non-resonant counterparts.
A problem is that for a non-resonant case the modulation frequencies must be low to provide a chamber pressure level detectable by the microphone. At low frequencies, external vibrational noise amplitudes are higher. Secondly, the wave nature of pressure propagation is not capitalized on. For a traveling sine wave, instantaneous nodes of zero pressure amplitude must be balanced by antinodes with a much higher pressure amplitude to maintain average energy density. The resulting larger amplitude provides a larger microphone signal, which is absent in the non-resonant case.
Like reference symbols in the various drawings indicate like elements.